# Unique determination of a time-dependent potential for wave equations from partial data

* Corresponding author
1 CPT - E8 Dynamique quantique et analyse spectrale
CPT - Centre de Physique Théorique - UMR 7332
Abstract : We consider the inverse problem of determining a time-dependent potential $q$, appearing in the wave equation $\partial_t^2u-\Delta_x u+q(t,x)u=0$ in $Q=(0,T)\times\Omega$ with $\Omega$ a $C^2$ bounded domain of $\mathbb R^n$, $n\geq2$, from partial observations of the solutions on $\partial Q$. We prove global unique determination of a coefficient $q\in L^\infty(Q)$.
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https://hal.archives-ouvertes.fr/hal-01154831
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Yavar Kian. Unique determination of a time-dependent potential for wave equations from partial data. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2017, 34 (4), pp.973-990. ⟨10.1016/j.anihpc.2016.07.003⟩. ⟨hal-01154831v2⟩

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